This book covers all principal aspects of currently investigated frustrated systems, from exactly solved frustrated models to real experimental frustrated systems, going through renormalization group treatment, Monte Carlo investigation of frustrated classical Ising and vector spin models, low-dimensional systems, spin ice and quantum spin glass. The reader can OCo within a single book OCo obtain a global view of the current research development in the field of frustrated systems.This new edition is updated with recent theoretical, numerical and experimental developments in the field of frustrated spin systems. The first edition of the book appeared in 2005. In this edition, more recent works until 2012 are reviewed. It contains nine chapters written by researchers who have actively contributed to the field. Many results are from recent works of the authors.The book is intended for postgraduate students as well as researchers in statistical physics, magnetism, materials science and various domains where real systems can be described with the spin language. Explicit demonstrations of formulas and full arguments leading to important results are given where it is possible to do so."

The field of highly frustrated magnetism has developed considerably and expanded over the last 15 years. Issuing from canonical geometric frustration of interactions, it now extends over other aspects with many degrees of freedom such as magneto-elastic couplings, orbital degrees of freedom, dilution effects, and electron doping. Its is thus shown here that the concept of frustration impacts on many other fields in physics than magnetism. This book represents a state-of-the-art review aimed at a broad audience with tutorial chapters and more topical ones, encompassing solid-state chemistry, experimental and theoretical physics.

Debashish Chowdhury's critical review of more than a thousand papers not only identifies the complexities involved in the theoretical understanding of the real spin glasses but also explains the physical concepts and the mathematical formalisms that have been used successfully in solving the infiniterange model. Originally published in 1987. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Frustrated spin systems have been first investigated five decades ago. Well-known examples include the Ising model on the antiferromagnetic triangular lattice studied by G H Wannier in 1950 and the Heisenberg helical structure discovered independently by A Yoshimori, J Villainn and T A Kaplan in 1959. However, extensive investigations on frustrated spin systems have really started with the concept of frustration introduced at the same time by G Toulouse and by J Villain in 1977 in the context of spin glasses. The frustration is generated by the competition of different kinds of interaction and/or by the lattice geometry. As a result, in the ground state all bonds are not fully satisfied. In frustrated Ising spin systems, a number of spins behave as free spins. In frustrated vector spin systems, the ground-state configuration is usually non-collinear. The ground state of frustrated spin systems is therefore highly degenerate and new induced symmetries give rise to unexpected behaviors at finite temperatures. Many properties of frustrated systems are still not well understood at present. Theoretically, recent studies shown in this book reveal that established theories, numerical simulations as well as experimental techniques have encountered many difficulties in dealing with frustrated systems. In some sense, frustrated systems provide an excellent testing ground for approximations and theories. Experimentally, more and more frustrated materials are discovered with interesting properties for applications.

Electric control of magnetic properties, or inversely, magnetic control of dielectric properties in solids, is called a magnetoelectric effect and has long been investigated from the point of view of both fundamental physics and potential application. Magnetic and dielectric properties usually show minimal coupling, but it recently has been discovered that magnetically induced ferroelectricity in some spiral magnets enables remarkably large and versatile magnetoelectric responses. To stabilize such helimagnetism, magnetic frustration (competition between different magnetic interactions) is considered the key. In the present work, two of the most typical frustrated spin systems—triangular lattice antiferromagnets and edge-shared chain magnets—have systematically been investigated. Despite the crystallographic simplicity of target systems, rich magnetoelectric responses are ubiquitously observed. The current results published here offer a useful guideline in the search for new materials with unique magnetoelectric functions, and also provide an important basis for a deeper understanding of magnetoelectric phenomena in more complex systems.

Spin glasses are disordered magnetic systems that have led to the development of mathematical tools with an array of real-world applications, from airline scheduling to neural networks. Spin Glasses and Complexity offers the most concise, engaging, and accessible introduction to the subject, fully explaining what spin glasses are, why they are important, and how they are opening up new ways of thinking about complexity. This one-of-a-kind guide to spin glasses begins by explaining the fundamentals of order and symmetry in condensed matter physics and how spin glasses fit into--and modify--this framework. It then explores how spin-glass concepts and ideas have found applications in areas as diverse as computational complexity, biological and artificial neural networks, protein folding, immune response maturation, combinatorial optimization, and social network modeling. Providing an essential overview of the history, science, and growing significance of this exciting field, Spin Glasses and Complexity also features a forward-looking discussion of what spin glasses may teach us in the future about complex systems. This is a must-have book for students and practitioners in the natural and social sciences, with new material even for the experts.

Magnetism is one of the most intriguing phenomena observed in nature. Magnetism is relevant to physics and geology, biology and chemistry. Traditional magnets, an ubiquitous part of many everyday gadgets, are made of heavy iron- or nickel based materials. Recently there have been reports on the observation of magnetism in carbon, a very light and biocompatible element. Metal-free carbon structures exhibiting magnetic ordering represent a new class of materials and open a novel field of research that could lead to many new technologies. · Thee most complete, detailed, and accurate Guide in the magnetism of carbon · Dynamically written by the leading experts · Deals with recent scientific highlights · Gathers together chemists and physicists, theoreticians and experimentalists · Unified treatment rather than a series of individually authored papers · Description of genuine organic molecular ferromagnets · Unique description of new carbon materials with Curie temperatures well above ambient.

Frustrated spin systems have been first investigated five decades ago. Well-known examples include the Ising model on the antiferromagnetic triangular lattice studied by G H Wannier in 1950 and the Heisenberg helical structure discovered independently by A Yoshimori, J Villainn and T A Kaplan in 1959. However, extensive investigations on frustrated spin systems have really started with the concept of frustration introduced at the same time by G Toulouse and by J Villain in 1977 in the context of spin glasses. The frustration is generated by the competition of different kinds of interaction and/or by the lattice geometry. As a result, in the ground state all bonds are not fully satisfied. In frustrated Ising spin systems, a number of spins behave as free spins. In frustrated vector spin systems, the ground-state configuration is usually non-collinear. The ground state of frustrated spin systems is therefore highly degenerate and new induced symmetries give rise to unexpected behaviors at finite temperatures. Many properties of frustrated systems are still not well understood at present. Theoretically, recent studies shown in this book reveal that established theories, numerical simulations as well as experimental techniques have encountered many difficulties in dealing with frustrated systems. In some sense, frustrated systems provide an excellent testing ground for approximations and theories. Experimentally, more and more frustrated materials are discovered with interesting properties for applications.

This book deals with a new class of magnetic materials, spin ice. Spin ice has become the canonical example of modern frustrated magnetism where competing interactions between spins set the rules for an emergent magnetostatic gauge field theory. Excitations take the form of magnetic monopoles or can condense via a Higgs mechanism. Beyond classical spin ice, the book describes the new physics emerging when quantum coherence (spin liquids, photon-like excitations) and itinerant electrons (anomalous Hall effect) are included in artificial systems. This first book dedicated to spin ice is a review of the current understanding of the field, both on the theoretical and experimental levels, written by leading experts. The book is written in a linear way with very few prerequisites. It also contains textbook-like descriptions of theoretical methods to help advanced students and researchers to enter the field.